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both support solving problems using factors and multiples.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},426336,1790919004,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":112},962084925636,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","ACT ® MATH CRAM SHEET  \nNUMBER CLASSIFICATION  \nRational Numbers  \nIntegers  \nWhole numbers  \nNatural numbers  \nEach number system is a subset another.  \nA rational number is also a real number, areal number is also a complex number, etc.  \n\n| Number Class | Definition | Examples |\n| --- | --- | --- |\n| Natural numbers | The number 1 or any number obtained by adding 1 to it one or more times. | 1, 2, 3, 4, 5,   |\n| Whole Numbers | Whole numbers do not include fractions or decimal parts and is a positive integer or zero. | 0, 1, 2, 3, 4, 5,   |\n| Integers | Any whole number or its opposite. |   , −5, −4, −3, −2,−1, 0, 1, 2, 3, 4, 5,   |\n| Rational numbers | A number can that be expressed as a ratio or fraction. | • 2/10 .6\u003Cbr>• 3/10\u003Cbr>• 2.957 |\n| Real Numbers | A number that has no imaginary part. All real numbers can be located on a number line. | • −92\u003Cbr>• 5/9\u003Cbr>• √2 |\n| Complex Numbers | a + bi where a and b are real numbers and i (imaginary number) is a formal square root of −1 (i= √-1, i2 = -1) | • -1 + 2i\u003Cbr>• 7-9i\u003Cbr>• -6i |\n\nNUMBER LINES  \n|2| |2|  \n-3 -2 -1 0 1 2 3  \nAbsolute Value  \nAbsolute value is the distance away from zero a number is on the number line. It is always positive and is written |x| .  \nFor example, the absolute value of 2 is written as |2| .  \nMATHEMATICAL SYMBOLS  \n\n| Phrase | Symbol |\n| --- | --- |\n| equal, is, was, will be, has, costs, gets to, is the same as, becomes | = |\n| times, of, multiplied by, product of, twice, doubles, halves, triples | × |\n| divided by, per, ratio of/to, out of | ÷ |\n| plus, added to, sum, combined, and, more than, totals of | + |\n| subtracted from, less than, decreased by, minus, difference between | − |\n| what, how much, original value, how many, a number, a variable | 􀀛 n etc., , |\n\nLesser Known Symbols  \nThe Golden Ratio: φ  \nInifinity: ∞  \nEuler’s Number: e Universal Quantifier: ∀  \nMembership Sign: ∈  \nACT ® MATH CRAM SHEET  \nPERCENTS, FRACTIONS, AND DECIMALS  \n\n| Percent Increase |  | Percent Decrease\u003Cbr>| × 100 | Percent to Fraction/Decimal\u003Cbr> Percentage\u003Cbr>100 |\n| --- | --- | --- | --- | --- |\n| | × 100 |  |  |  |\n\n\n| Fraction to Decimal\u003Cbr>numerator\u003Cbr>denominator | Fraction to Percent\u003Cbr>|\n| --- | --- |\n\n\n| Decimal to Fraction |  |  |  | Decimal to Percent\u003Cbr>decimal × 100 |\n| --- | --- | --- | --- | --- |\n| decimal\u003Cbr>1 | × | 10 n\u003Cbr>10 n | \u003Cbr>n is the number of places behind the decimal point\u003Cbr>|  |\n\nRATIOS AND PROPORTIONS  \nRatios of Two Items  \n\n| Items | Ratio | Fraction | Written | Simplified Ratio |\n| --- | --- | --- | --- | --- |\n| 6 oranges, 8 apples | 6:8 | 6/8 | 6 oranges to 8 apples | 3:4 |\n| 8 trains, 14 cars | 8:14 | 8/14 | 8 trains to 14 cars | 4:7 |\n| 4 feet, 3 feet | 4:3 | 4/3 | 4 feet to 3 feet | 4:3 |\n\n\n| Ratios |  |  |  |  |\n| --- | --- | --- | --- | --- |\n|  | Part to part |  | Part to whole |  |\n|  | 2:1 | 1:2 | 2:3 | 1:3 |\n|  | 2/1 | 1/2 | 2/3 | 1/3 |\n|  | 2 to 1 | 1 to 2 | 2 to 3 | 1 to 3 |\n\n\n| Proportions |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| | 3:4 | = | 6:8 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n|  | 3:4 | :: | 6:8 |  |  |  |  |  |  |\n|  |  |  |  | |  |  |  |  |  |\n|  | 3 is to 4 | as | 6 is to 8 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |\n\n\n| Calculating Proportions |  |  |\n| --- | --- | --- |\n| 6\u003Cbr>2 | = | 12\u003Cbr>? |\n| \u003Cbr>24 6\u003Cbr>÷6\u003Cbr>\u003Cbr>6\u003Cbr>=\u003Cbr>2\u003Cbr>4 = x\u003Cbr>|  |  |\n| 6 12 ~~ ~~ = ~~ ~~\u003Cbr>2 4 |  |  |\n\nACT ® MATH CRAM SHEET  \nFACTORS  \nWhat is a factor?  \nA whole number is a factor of another whole number if it divides it evenly.  \n\n| Greatest common factor (GCF)\u003Cbr>The greatest common factor of two or more whole numbers is the largest number that is a factor of them all. | 7: 1, 7 \u003Cbr>28: 1, 2, 7, 14 \u003Cbr>GCF: 7 | Factor Tree\u003Cbr>28\u003Cbr>2 14\u003Cbr>2 7\u003Cbr>|\n| --- | --- | --- |\n\nMULTIPLES  \nWhat is a multiple?  \nA whole number is a multiple if it is the result of multiplying another whole number by an integer.  \n\n| Least Common Multiple (LCM)\u003Cbr>The le","cbCaivf8ULWU7ZUz","https://ap.wps.com/l/cbCaivf8ULWU7ZUz","pdf",3754278,12,"English","# Number Classification\n## Number Lnes and Absolute Value\n# Mathematical Symbols\n# Percents, Fractions, and Decimals\n# Ratios and Proportions\n# Factors and Multiples\n# Permutation and Combination\n# Scientific Notation","[{\"question\":\"What number sets are included in this ACT math cram sheet?\",\"answer\":\"It covers natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers, emphasizing how each set relates as a subset of another.\"},{\"question\":\"How is absolute value defined and written?\",\"answer\":\"Absolute value is the distance from zero on the number line and is always positive, written as |x|.\"},{\"question\":\"What are GCF and LCM, and how do they connect to factors and multiples?\",\"answer\":\"GCF is the greatest common factor shared by whole numbers, while LCM is the least common multiple shared by them; both support solving problems using factors and multiples.\"}]","ACT Math Cram Sheet - Math Number Systems & Symbols - Study Guide | PDF",1790640242]